Sixty years ago the late William S. Robinson (1913–96) published his Ecological Correlations and the Behaviors of Individuals. 1 The paper became an all-time classic and it is one of the most influential methodological papers in social sciences. To underscore its impact on epidemiology , this classic was reprinted in this journal, 2 along with an original re-analysis of Robinson's data and conc...

Through this study, the ability of a modified Peng-Robinson (MPR) equation of state in predicting the surface tension of n-alkanes based on the density functional theory approach was investigated and compared with other studies. The interfacial layer thickness and the density profile were calculated simultaneously at different temperatures from triple point to near critical point using the modi...

We introduce a set of operations that we call crystal operations on matrices with entries either in {0, 1} or in N. There are horizontal and vertical forms of these operations, which commute with each other, and they give rise to two different structures of a crystal graph of type A on these sets of matrices. They provide a new perspective on many aspects of the RSK correspondence and its dual,...

We interpret geometrically a variant of the Robinson-Schensted correspondence which links Brauer diagrams with updown tableaux, in the spirit of Steinberg’s result [32] on the original Robinson-Schensted correspondence. Our result uses the variety of all (N , ω, V) where V is a complete flag in C2n, ω is a nondegenerate alternating bilinear form on C2n, and N is a nilpotent element of the Lie a...

A Richardson variety X α in the Orthogonal Grassmannian is defined to be the intersection of a Schubert variety X in the Orthogonal Grassmannian and a opposite Schubert variety Xα therein. We give an explicit description of the initial ideal (with respect to certain conveniently chosen term order) for the ideal of the tangent cone at any T -fixed point of X γ α, thus generalizing a result of Ra...

We consider the Brascamp–Lieb inequalities concerning multilinear integrals of products of functions in several dimensions. We give a complete treatment of the issues of finiteness of the constant, and of the existence and uniqueness of centred gaussian extremals. For arbitrary extremals we completely address the issue of existence, and partly address the issue of uniqueness. We also analyse th...

In F. Caselli (Involutory reflection groups and their models, J. Algebra 24:370–393, 2010), a uniform Gelfand model is constructed for all nonexceptional irreducible complex reflection groups which are involutory. Such models can be naturally decomposed into the direct sum of submodules indexed by Sn-conjugacy classes, and we present here a general result that relates the irreducible decomposit...

Schützenberger’s theorem for the ordinary RSK correspondence naturally extends to Chen et. al’s correspondence for matchings and partitions. Thus the counting of bilaterally symmetric k-noncrossing partitions naturally arises as an analogue for involutions. In obtaining the analogous result for 3-noncrossing partitions, we use a different technique to develop a MAPLE package for 2-dimensional v...